where the vectors \({f}_n\)  represent spherical wave expansion coefficients and the transition matrix \({T}\)  maps regular spherical waves onto outgoing spherical waves [1]}. The equivalence of eigenvalue problems (REF ) and (REF ) is detailed Appendix  and is based on a relation between the transition matrix and scattering dyadic
\(T_{\alpha \beta } = \int \limits _{4\pi } \int \limits _{4\pi } _\alpha ^\ast ({r}) \cdot S̭({r},{r}^{\prime }) \cdot _\beta ({r}^{\prime }) ^{\prime },\) 
